Born to count: a biological basis of mathematics

Abstract

As languages, mathematics is a biological product and thus based on causal processes of two time scales, namely neural mechanisms and evolution. In this commentary, I will try to figure out possible scenarios responsible for the chick mathematics raised by the target article, focusing on discreteness and transposability of natural numbers.

Suppose I talked to a mathematician who recently published a big thesis. The paper was long, and full of strange symbols and equations that I never understood. “I found it!” He said and was so excited trying to explain how important this was. Embarrassed, I replied to him stupidly, “you invented a new style, right?” He shrugged wordlessly.

For most good mathematicians, as he is, mathematics is a natural science. The theorem existed before he proved it, and it is true ever and forever. I simply misunderstood him. If findings of an experimental biologist were blamed as artifacts because the lab bench was full of industrial bottles of pure chemicals? Mathematicians try to find nature by inventing new tools and logic. The theorem was hidden but now found through skilled inventions as argued by Livio (2009).

How about the chicks? Most striking point in this feature article by Lorenzi et al. (2025) is that the number sense, as would be a core of abstract mathematical thinking, is a predisposed innate nature in newly hatched chicks and zebrafish with no preceding experiences. They do not learn numbers (natural numbers) but are born to count. If mathematics is universal, why not for chicks and zebrafish?

Natural numbers and discrete acts

Counting numbers is a discrete act and not continuum. Acts are generally discrete in behavioral execution. We don’t smile and rage at a time. Contractions of facial muscles are coordinated in totally distinct fixed action patterns. As a dice never shows two faces at a time, CNS mechanisms do not allow two different action patterns to coincide. In the “Study of Instinct”, Tinbergen hypothesized hierarchical control system composed of mutually exclusive centers at the level of consummatory acts (Chapter 5, An attempt at a synthesis; Tinbergen 1949). In different contexts, a single neural network yields distinct output patterns (Harris-Warrick and Flamm 1986). Otherwise, competitive interactions among networks could be responsible for the discrete acts (Pirger et al. 2014). If prefrontal cortex and its functional analogues in other animals were the key in this orchestration? Convergent inputs to NCL (birds, Güntürkün and Bugnyal 2016) or prefrontal/cingulate cortex (mammals, Tanji 1994), their efferent controls (arcopallium and supplementary motor cortex, in chicks and humans, respectively) might be involved.

In addition, numbers are multifaceted. Number system could represent totally different contexts, such as amount, order and operators. Two apples (algebra), the apple placed in the second place (geometry), double the apples (arithmetic). All two but they are distinct. Chicks appear to do all of them, suggested that the multifaceted nature is also predisposed and prelinguistic. Number neurons must therefore be examined in other behavioral contexts where discrete acts are triggered coincidentally.

Prime numbers and geometric symmetry

Mathematics is composed of several subfields, such as algebra, geometry, and calculus. A hard problem in a subfield can be solved, as often represented in a much easier way in the other. Transportability is another key character of mathematics, if not to mention their “unreasonable effectiveness” in physics and all other natural sciences (Wigner 1960). A similar nature has also been pointed out in chicks, as orderly numbers have a mental representation in space (Vallortigara 2017).

Another case could be found in prime numbers. To see if the given number is prime, lack of reducibility must be examined by each of all the numbers below. It is a hard job but we have no other means to see. When viewed geometrically, namely if the number was represented by a group of dots, prime numbers are odd and asymmetrical, whereas all other nonprimes can be symmetrically arranged in space. As far as small prime numbers are concerned, it appears to be the chicks’ way to perceive primes (Loconsole and Regolin 2022). Actually, the visual perception of symmetry is widespread. Capability to visually detect bodily symmetry is associated with successful mate choice in female swallows (Møller 1992) as well as in humans (Thornhill and Gangestad 1999). Though we must be cautious as to whether the cognitive map of visual features is formed as a low-dimensional canonical Cartesian space with normal distance (Ono et al. 2002), transposability could have a biological basis as it was selected for reproductive success.

Conclusion

Fertilized cells, after 3 weeks of incubation, are born to count. The chick mathematics is shaped through two biological processes, namely ontogeny and phylogeny. Evo-devo studies of the underlying neuro-cognitive processes would be a key toward understanding the biological bases of mathematics.

Author contributions

Toshiya Matsushima (Writing—original draft).

Funding

None declared.

Conflict of interest statement: The author declares no conflict of interest in this commentary.

References